Measuring Educational Poverty in Italy: A Multi-Dimensional and Fuzzy Approach

Gaia Bertarelli, Antonella D’Agostino, Caterina Giusti and Monica Pratesi1


In the past few years, educational poverty (EP) has emerged on the political agenda of several countries as a new social challenge that urgently needs to be addressed. In fact, it has been widely recognised that deprivation in education can determine a gap at a particularly vulnerable time of life that is not easy to reverse later. In its law in the 2018 budget, the Italian government introduced an experimental fund to fight EP through the removal of the economic, social and cultural obstacles that prevent the full educational achievement of minors and young adults. To provide an adequate measure of EP in Italy, the Italian National Statistical Institute (Istat) (Quattrociocchi, 2018) defined a multi-dimensional Educational Poverty Index (EPI), which measures material, relational, cultural and environmental problems that limit the ability of young people to live in a complex society. The EPI measures the overall level of EP for individuals ages 15-29, using several data sources and providing a territorial disaggregation of the Italian regions (at the NUTS 2 level). To aggregate the single indicators defining the four dimensions of the EPI - participation, resilience, standard of living and friends and skills - Istat relied on an adjusted Mazziotta-Pareto index (Mazziotta and Pareto, 2016, 2018).

Several authors have proposed alternative EP measures (Checchi, 1998; Brandolini and D’Alessio, 1998; Allmendinger, 1999; Allmendinger and Leibfried, 2003; Watkins, 2000). Checchi (1998) expressed the concept of EP within the framework of the capability approach. Brandolini and D’Alessio (1998) referred to the concept of poverta d’istruzione as a reference point in the discussion of education as a separate function in addition to health, social relations, labour market status, housing and economic resources. Allmendinger (1999) stressed the need to take into account the material and non-material aspects of social deprivation and referred explicitly to the living conditions approach. Watkins (2000) explored the link between educational deprivation and poverty.

In more recent empirical studies, EP has evolved into a multi-dimensional concept, linked to the idea of deprivation, for children and adolescents, of the ability to learn, experiment and develop and freely expand their skills, talents and aspirations (Save the Children, 2018). Lohman and Ferger (2014) discussed the concept of EP within the context of changes in the welfare state. Larysa and Felice (2016) applied multidimensional index of deprivation in the analysis of cognitive skills. Agasisti et al. (2020) addressed the issue of multi-dimensional poverty measures for analysing EP.

Pratesi et al. (2020) proposed the use of small area estimation methodologies to estimate the multi-dimensional index proposed by Istat, the EPI, at the sub-regional level, as local measures of EP can be crucial in tailoring policy actions in the places where people live. Specifically, the paper considered the local level, represented by the intersection between the Italian regions (NUTS 2 level) and the degree of urbanisation designated by Eurostat by the DEGURBA three-level classification (cities, towns and suburbs and rural areas). The motivating idea was to explore the potential role played by the degree of urbanisation in disentangling the EP measurement. Indeed, the work highlighted the presence in the same region of the same critical areas with high EP, together with areas with low EP.

In this chapter, we extend Pratesi et al. (2020) by providing a fuzzy multi-dimensional measure of EP based on the EPI. We limit our analysis to the previous EP dimensions, measured by the AVQ survey. Quattrociocchi (2018) included digital as well as literacy and quantitative skills in the dimension ‘friends and skills’. Although we include digital skills indicators using the AVQ survey, we do not include literacy and quantitative skills in our analysis because these two skills are not collected in the AVQ survey.2 Therefore, as explained above, in this chapter we approximate outcomes for these two education skills using the individual level of education attained.

Our first step is therefore to explore the fuzzy nature of the phenomenon as it results from the four dimensions, using only AVQ data. Indeed, as the EPI is a multi-dimensional index, the integrated fuzzy and relative (IFR) methodology can be used under the assumption that EP is a vague predicate manifested in different shades and degrees (fuzzy concept), rather than an attribute that is simply present or absent for individuals, as in the approach developed by Istat. Our aim is therefore to measure the degree of EP in the Italian regions and in the local areas at the intersection of the regions with the DEGURBA classification by defining an overall EP fuzzy measure and four EP dimension-specific measures.

The chapter is organised as follows. First, we present the data and the indicators used to define the EP multi-dimensional measure. Second, we summarise the methodology used before presenting the main findings from the analysis. Finally, we offer some concluding remarks and future extensions of our work.

168 Bertarelli, D’Agostino, Giusti and Pratesi Dimensions of EP and Data

The EPI defined by Istat is a multi-dimensional index that identifies four dimensions of EP for people aged 15 to 29:

  • • participation, meaning the lack of participation in social life;
  • • resilience, meaning a lack of development in an attitude of trusting oneself and one’s abilities;
  • • standard of living, meaning a lack of opportunity to lead an inclusive, healthy and safe life with an adequate standard of living;
  • • friends and skills, meaning the lack of opportunity to form relationships with others and to achieve the skills (digital, literacy and quantitative skills) needed to succeed in the current fast-paced world.

The indicators currently used by Istat to measure deprivation in terms of these four dimensions come from several data sources (Quattrociocchi, 2018). In this chapter, following Pratesi et al. (2020) and due to the availability of data, we use only items from the ‘aspects of everyday life’ (AVQ) survey in 2016 (Istat, 2019).

Based on this source, the indicators used by Pratesi et al. (2020) to measure EP are illustrated in Figure 11.1 with rectangles, arranged in the four dimensions, which are depicted by ovals. In this framework, each indicator is a dichotomous variable defined by 53 different items in the AVQ survey.

For example, the indicator that measures the lack of ‘political participation’ - i.e. the percentage of people who do not engage in political activity - is binary and is defined on the basis of the following four items in the AVQ questionnaire, indicating whether an individual has taken the opportunity to:

  • 1. attend a political rally at least once in the past 12 months;
  • 2. participate in a political procession at least once in the past 12 months;
  • 3. engaging in free activity for a party at least once in the past 12 months;
  • 4. donate money to a party for either membership or support at least once in the past 12 months.

To organise our research and refine our concept of EP, we use the four dimensions articulated by Pratesi et al. (2020), but our empirical analysis is based directly on the 53 individual items arranged along these four dimensions. In this way, we preserve the richness of the data. This means that the items previously mentioned are 4 of the 53 items used in our empirical analysis.’’ Among the items we use is the educational level attained as an indicator of educational outcomes to proxy for competence scores in the ‘friends and skills’ dimension. Because in its Europe 2020 Strategy the European Union (EU) defines those who have an ISCED 0-2 qualification as early school leavers, we use this as a criterion in an EP threshold (Lohmann and Ferger, 2014). Nevertheless, our sample also includes individuals who

Framework adopted by Pratesi et al. (2020). Note

Figure 11.1 Framework adopted by Pratesi et al. (2020). Note: Indicators (rectangles) arranged in the four dimensions (ovals) of the EPI from the AVQ survey.

are still enrolled at compulsory school, so we consider people deprived only if they are not currently enrolled in an ISCED 3 course.

The final data set used in the empirical analysis covers 5,093 individuals aged 15-29 for whom all 53 items were available.4 To map EP in Italy, we consider the 20 Italian regions.

For each region. Table 11.1 summarises the sample population of those aged 15-29, together with some descriptive statistics computed on this sub-sample, excluding those with missing values. The size of the sample population in the regions varies from a minimum of 106 (Valle d’Aosta) to a maximum of 537 (Campania). The gender composition is quite stable across the regions, varying from 47% males in Trentino-Alto Adige to 54% in Friuli Venezia Giulia. The other statistics considered concern the age of the sample population, namely the mean, the coefficient of variation (CV) and the percentage of people aged 20 or younger. Although the average age and the corresponding CV did not vary much across the regions, we observed more heterogeneity among people less than 20 years old, from 24% in Valle d’Aosta to 34% in Marche.

Table 11.1 Descriptive statistics across the regions, listed from north to south and then the islands


% Males

Mean age

CV age

% age < 20







Valle d’Aosta












Trent. Alto Adige












Friuli Venezia Giulia


























































































Following Pratesi et al. (2020), we also considered a finer geographic disaggregation, through the intersection of the regions with the DEGURBA degree of urbanisation, as follows:

  • • densely populated areas (cities, large urban areas);
  • • moderately densely populated areas (towns and suburbs, small urban areas);
  • • thinly populated areas (rural areas).

This cross-classification results in a total of 59 target areas, as Valle d’Aosta has no densely populated areas. The sample size varies from a minimum of 11 (densely populated areas in Marche) to a maximum of 365 (densely populated areas in Campania). Given the smaller sample size in several of these areas, Pratesi et al. (2020) used small area methods to obtain reliable estimates. In this chapter, we mainly aim to derive a fuzzy measure of EP in 20 regions. We also use DEGURBA areas to explore the potential differences across the regions. Nevertheless, because of the small sample size, the results of this finer geographic disaggregation require further analysis.


As explained in the previous sections, EP is a complex phenomenon which includes different dimensions that are not usually measured directly. Its multi-dimensional nature implies that children or individuals experience a certain number of observed deprivations that can be summarised into this set of latent dimensions. Moreover, EP can be treated as a matter of degree, replacing the simple dichotomy (0,1) - presence/absence of EP - with a certain degree of EP, which varies between 0 (not deprived at all) to 1 (completely deprived) for each dimension.

In this chapter, we apply multi-dimensional and fuzzy logic (Zadeh, 1965) to study EP at the NUTS 2 (region) level and use the DEGURBA classification in Italy. In particular, we adapt the methodology called IFR (Betti et al., 2006) to this framework. See Betti et al. (2020) for an interesting literature review of this methodology. The positive results that have been achieved by applying the IFR approach to fields other than poverty (see e.g. Aassve et ah, 2007; Betti et ah, 2011; Betti and Lemmi, 2013; Betti et ah 2016; D’Agostino et ah, 2019) demonstrate its applicability and robustness.

Let Ik be the single item associated with the observed indicator k (k = 1, ..., K, with К = 53) in the AQV survey converted into the range [0,1]. Following Quattrociocchi (2018), we define four different latent dimensions (s = 1, ..., S with S = 4). Each dimension s is composed of a different number of items Ik (k = 1, ..., КJ, as illustrated above. We calculate a function, called a membership function, for each dimension s, which is a quantitative specification of the individual degree of EP between 0 and 1, in which the lowest level of EP takes a value of 0 and the highest level takes a value of 1.

Let EPis)j indicate the membership function of dimension s for individual j (/=1 ... n) in the sample, calculated as:

where w{s)k is the weight of Ik in dimension s. In turn, w{s]k is calculated as the product of two components that take into account both the dispersion of Ik in dimension s and its correlation with the other indicators in the same dimension s (see Betti et al., 2006). According to Equation 11.1, as the value of EP increases from 0 to 1, the EP of individual / in the corresponding dimension increases. Finally, a comprehensive measure of EP for each individual / is calculated as the unweighted mean of the S dimensions in the dimension-specific EP,s]j.

Finally, the weighted sample means EP(S) (s = 1, ..., S) in Equation (11.1) and EP in Equation (11.2) measure the degree of EP observed at the regional level in each dimension s and for all four dimensions as a whole, respectively. In other words, EP is indeed a single composite index, which we call the Educational Poverty Fuzzy Indicator (EPFI), and each EPS represents a single dimension-specific composite index (Betti et al., 2020). For the sake of simplicity, in the empirical analysis we call these dimension- specific indices EPF_Participation, EPF_Resilience, EPF_Standard of living and EPF_Friends and skills.

Findings: A Comparative Regional Perspective

In this section, we offer findings after using the multi-dimensional and fuzzy measures of EP discussed earlier.

The main goal of this analysis is to provide an overview of the current degree of EP from a cross-regional perspective using EPFI and the dimensional indicators EPF_Participation, EPF_Resilience, EPF_Standard of living and EPF_Friends and skills. In addition, we also outline some findings using the DEGURBA classification, even though, as stressed above, we comment on the results only if the area has a sufficient number of sample units. Figure 11.2 is a map of Italy in which the colour of each region

EPFI at the regional level

Figure 11.2 EPFI at the regional level.

depends on the degree of EP. The map shows a range of colours from white to black to indicate the degree of EP from low to high. Specifically, the value of EPFI is in the range [0,1], in which the maximum degree of EP equals 1.

The map, as expected, illustrates a clear divide between the northern/central and southern regions, in which the northern/central regions are characterised by lower levels of EP. The lowest EPFI is observed in Trentino-Alto Adige, where it is 0.36, whereas the four southern regions (Puglia, Sicilia, Calabria and Campania) have the highest levels of EPFI, with increasing intensity: the value of EPFI ranges from 0.47 in Puglia to 0.52 in Campania. Therefore, the EP issue adds to the Italian north/south divide in economic performance and living standards, which remains an unresolved issue in Italian economics and politics. A discussion on its multi-dimensional shape is certainly useful in facilitating a better understanding of EP. The maps in Figure 11.3 summarise the results obtained with respect to each of the four dimensions.

Looking at each dimension leads to further discussion. The four dimensions show some heterogeneity among them and across regions. In other words, the degree of EP in each region seems to vary in intensity across the dimensions. These findings demonstrate the importance of taking into account the multi-dimensional nature of EP. In particular, the dimension ‘Participation’ (see the EPF_Participation map in Figure 11.3) shows the participation of the youngest people in social life. The degree of deprivation in this dimension seems to be generally very low in Tuscany, for instance, while ‘Standard of living’ (see the EPF_Standard of living map in Figure 11.3) has the highest value, meaning that young people are more deprived with respect to this aspect of EP. Campania and Calabria have the highest value of the indices in each dimension and Sicily in three out of four dimensions. In these regions, therefore, young people suffer multiple types of deprivation, with a similarly high degree of intensity. The situation in Lombardy is also very interesting. Young people seem to be very deprived in terms of the dimension ‘resilience’, illustrating the development of an attitude of trusting oneself and one’s abilities, whereas they suffer less in the ‘participation’ dimension. This could be a consequence of the geographic heterogeneity of the region, which may correspond with the presence of different areas according to the DEGURBA classification, as we explore below.

These findings, while highlighting numerous economic and social challenges that lie ahead, at the same time provide some guidelines on which educational policies and practices should be addressed by policymakers to reduce geographic differences in EP. The ability to further disaggregate the results using a more detailed geographic classification, namely using the DEGURBA regional classification as in Pratesi et al. (2020), is useful from a policy perspective. However, when this classification is used, the small sample size in some areas suggests the need to use small area estimation techniques, as done by Pratesi et al. (2020) in estimating the EPI index defined by Istat. Accordingly, the results obtained here using the DEGURBA

Degree of EP at the regional level in the four EPFI dimensions

Figure 11.3 Degree of EP at the regional level in the four EPFI dimensions.

regional classification for EPFI should be interpreted as an example of the utility of a disaggregated analysis in studying EP.

The map in Figure 11.5 summarises the EPFI using the DEGURBA by regional classification. Figure 11.4 is a useful tool for representing the DEGURBA classification of Italy: cities are in dark grey, towns and suburbs in an intermediate shade of grey, and rural areas are in light grey. The regional boundaries are indicated by thick black lines.

Although some regions have no differences in EPFI values among the DEGURBA areas (e.g. in almost all southern regions), some of them, especially Emilia-Romagna, Lombardy, Marche and Friuli Venezia Giulia, have different gradations in colour, suggesting that EP varies across these areas. For instance, in Emilia-Romagna the results suggest that EP is more salient in rural areas than in the cities, and a similar conclusion can be reached about Marche.

A DEGURBA regional classification of Italy

Figure 11A DEGURBA regional classification of Italy: cities (dark grey), towns and suburbs (intermediate shade of grey), and rural areas (light grey). The thick black lines indicate regional boundaries.

EPFI using the DEGURBA regional classification

Figure 11.5 EPFI using the DEGURBA regional classification.

Some Final Remarks

In this chapter, we measure EP in Italy from a comparative perspective. First across regions and then using the DEGURBA regional classification.

We introduce a new approach for measuring EP. Indeed, we diverge from the common definition of EP as a level of education which falls below a threshold considered the minimum in a given society (Checchi, 1998; Allmendinger, 1999). In contrast, we treat EP as a multi-dimensional phenomenon composed of different dimensions, which are not directly measurable and are characterised by different degrees of intensity. That is, EP is a fuzzy measure.

For this reason, our approach also diverges from the approach used by Pratesi et al. (2020): although we use the same multi-dimensional definition of EP and the same dataset, this chapter uses a completely different methodological approach.

We computed a fuzzy index (EPFI) and 4D-specific fuzzy indices on the sample represented by individuals aged 15-29 using micro-data from the survey ‘Aspects of Everyday Life’ (AVQ) (Istat, 2019). Each indicator takes a value in the range [0,1], with 1 indicating the maximum degree of EP, and 0 the lowest.

Despite some limitations in the data, related to the impossibility of covering all items used by Istat (Quattrociocchi, 2018), the AVQ survey has many useful items for measuring EP in Italy. Thus, we use it to analyse EP in a multi-dimensional framework using only one source of micro-data. This is particularly important in the Italian case, where the lack of surveys on children and adolescents highly limits our ability to conduct a deep analysis on EP in a multi-dimensional framework using micro-data. Therefore, our analysis also aims to reflect the need for a useful cross-national survey to measure and monitor EP in its multi-dimensional shape. This national survey could be especially important for policymakers and practitioners and should be used to design more precise social policies. The results presented here reflect the fact that the regions and the DEGURBA areas have different degrees of EP and that even single dimensions show different levels of intensity in the same area.

From the policymaking perspective, the results of our analysis demonstrate the actual consistency and dimensions of EP at a useful local level, which in turn, suggest, for example, a revision of local governments’ normal policies employed to reverse EP.

From a methodological point of view, taking a fuzzy perspective on EP attains particular significance in our multi-dimensional approach. Indeed, it overcomes the issue of transforming each single indicator used in the analysis into a simple dichotomous variable to indicate the percentage of people who are deprived with respect to each specific aspect, as implied by the approach taken by Mazziotta-Pareto (2018). In summary, the fuzzy approach preserves the richness of the original data and includes a concept of vagueness and a measurement of relative poverty; thus, it is very useful for describing the multi-faceted nature of EP.

Our approach is not intended to replace the one proposed by Quattrociocchi (2018), which uses the Mazziotta-Pareto aggregation, but aims to enrich the existing information on EP. In fact, whereas the Istat EPI index gives the distribution of EP in each area compared with the national average, our proposed fuzzy index, EPFI, provides information about the intensity of EP in each area. Our analysis has three main limitations. First, although school results by themselves do not describe the concept of EP - which is more complex and related to the individual growth - it is also true that individual skills and abilities can be considered separate potential items in the definition of EP dimensions. As this was not possible in this study, it is an interesting development to be explored in future work.

Second, our analysis does not provide standard errors of the calculated fuzzy measures. Although it is good practice to do so, this procedure requires information on the primary sampling units, rotational groups and strata, which are not available in the user database of the AVQ survey. Last, it would be useful to investigate the four EP dimensions defined by Istat and used in this chapter in order to explore other possible multi-dimensional definitions of EP under a fuzzy approach.


  • 1 Acknowledgment: The work of Bertarelli, Giusti and Pratesi has been carried out with the support of the Project InGRID-2, European Project G.A. No. 730998.
  • 2 The information on literacy and quantitative skills can be inferred by using the Programme for the International Assessment of Adult Competences (PIAAC) survey. But the use of this information at the micro-level implies previous probabilistic linkage between the AVQ and PIAAC surveys.
  • 3 The full list of the items is available from the authors upon request.
  • 4 Because some of the items have missing values, the final analysis consists of 80% of the initial sample of those aged 15-29.


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